Quadrant method, group 11-19

General information group 11 - 19

Magic squares of group 10-18 are constructed by means of combining a grid consisting of H- and/or K-quadrants (each quadrant contains 2 times 8 digits), and a grid consisting of A-,B- and C-quadrants (each quadrant contains 4 times 4 digits).

Half of the amount of homogeneous H-grids (HHHH-grids) can be matched with homogeneous A- and with homogeneous C-grids, the other half can be matched

with mixed AC-grids.

Analogously half of the homogeneous K-grids can be matched with homogeneous B- and with homogeneous C-grids, the other half can be matched with mixed BC-grids.

Analogously half of the mixed HK- or KH-grids can be matched with mixed AC- and BC-grids, the other half can be matched with mixed ACC*B- or CABC*-grids.

Illustration group 11

Magic squares of group 10 are constructed by means of combining H-grids with A-grids.

In the example below a row grid with H4 in all four quadrants has been chosen.

H4 (row grid)

0	5	2	7	0	5	2	7
6	3	4	1	6	3	4	1
5	0	7	2	5	0	7	2
3	6	1	4	3	6	1	4
0	5	2	7	0	5	2	7
6	3	4	1	6	3	4	1
5	0	7	2	5	0	7	2
3	6	1	4	3	6	1	4

Now the construction of the matching column grid. Fill the top left quadrant after A1, A2, or A3. In the example A1 has been chosen. (Verify that A1*, A2* and A3* do not not work!).

A1 (column grid), step 1

0	7	6	1
7	0	1	6
1	6	7	0
6	1	0	7

In the 5th row only 1-6-7-0 is possible. And now you will find out that the third quadrant can only be completed with an A-structure.

A1 (column grid), step 2

0	7	6	1
7	0	1	6
1	6	7	0
6	1	0	7
1	6	7	0
7	0	1	6
0	7	6	1
6	1	0	7

The right half of the row grid must be filled with the digits 2, 3, 4, and 5. In column 5 it is only possible to fill in 2-5-3-4, or 4-3-5-2 . In the example 4-3-5-2 has been chosen. With both options you can only finish the upper right quadrant successfully when maintaining the A-structure. The down right quadrant follows automatically, and has necessarily also the A-structure.

A1 (column grid), step 3

0	7	6	1	4	3	2	5
7	0	1	6	3	4	5	2
1	6	7	0	5	2	3	4
6	1	0	7	2	5	4	3
1	6	7	0
6	1	0	7
0	7	6	1
7	0	1	6

A1 (column grid), step 4

0	7	6	1	4	3	2	5
7	0	1	6	3	4	5	2
1	6	7	0	5	2	3	4
6	1	0	7	2	5	4	3
1	6	7	0	5	2	3	4
6	1	0	7	2	5	4	3
0	7	6	1	4	3	2	5
7	0	1	6	3	4	5	2

In total there are 3 (A1, A2, A3) x 2 (options of step 3) = 6 different column grids.

Finally you can combine row and column grid to produce the magic square. The square below contains the X magic property (shown in blue).

1x digit from row grid +1 + 8x digit from column grid = most perfect 8x8 magic square

0	5	2	7	0	5	2	7	0	7	6	1	4	3	2	5	1	62	51	16	33	30	19	48
6	3	4	1	6	3	4	1	7	0	1	6	3	4	5	2	63	4	13	50	31	36	45	18
5	0	7	2	5	0	7	2	1	6	7	0	5	2	3	4	14	49	64	3	46	17	32	35
3	6	1	4	3	6	1	4	6	1	0	7	2	5	4	3	52	15	2	61	20	47	34	29
0	5	2	7	0	5	2	7	1	6	7	0	5	2	3	4	9	54	59	8	41	22	27	40
6	3	4	1	6	3	4	1	6	1	0	7	2	5	4	3	55	12	5	58	23	44	37	26
5	0	7	2	5	0	7	2	0	7	6	1	4	3	2	5	6	57	56	11	38	25	24	43
3	6	1	4	3	6	1	4	7	0	1	6	3	4	5	2	60	7	10	53	28	39	42	21

The total amount of squares of group 10 is: 48 (row grids H) x 6 (column grids) x 2 (swapping row and column grids) = 576; 24 x 6 = 144 of these squares have the extra magic property X.

Illustration group 12

Magic squares of group 12 are constructed by means of combining H-grids with C*-grids .

In the example below the same row grid as above (H4 repeated in all four quadrants) has been chosen.

H4 (row grid)

0	5	2	7	0	5	2	7
6	3	4	1	6	3	4	1
5	0	7	2	5	0	7	2
3	6	1	4	3	6	1	4
0	5	2	7	0	5	2	7
6	3	4	1	6	3	4	1
5	0	7	2	5	0	7	2
3	6	1	4	3	6	1	4

Now you put C1*, C3* or C5* in the upper left corner (verify that C2*, C4* and C6* will not work in giving a matching column grid). In the example C1* has been chosen.

C1* (column grid), step 1

0	7	6	1
6	1	0	7
1	6	7	0
7	0	1	6

In the 5th row you have only the matching option 1-6-7-0. And you only can finish the third quadrant successfully when maintaining the C*-structure.

C1* (column grid), step 2

0	7	6	1
6	1	0	7
1	6	7	0
7	0	1	6
1	6	7	0
7	0	1	6
0	7	6	1
6	1	0	7

The right half of the row grid must be filled in with the digits 2, 3, 4, and 5. Column 5 needs 2-4-3-5 or 4-2-5-3. In the example 2-4-3-5 has been chosen. With both options you can successfully finish the upper right quadrant only when continuing the C*-structure. The down right quadrant follows automatically, and has necessarily the C*-structure.

C1* (column grid), step 3

0	7	6	1	2	5	4	3
6	1	0	7	4	3	2	5
1	6	7	0	3	4	5	2
7	0	1	6	5	2	3	4
1	6	7	0
7	0	1	6
0	7	6	1
6	1	0	7

C1* (column grid), step 4

0	7	6	1	2	5	4	3
6	1	0	7	4	3	2	5
1	6	7	0	3	4	5	2
7	0	1	6	5	2	3	4
1	6	7	0	3	4	5	2
7	0	1	6	5	2	3	4
0	7	6	1	2	5	4	3
6	1	0	7	4	3	2	5

In total there are 3 (C1*, C3* or C5*) x 2 (options of step 3) = 6 different column grids.

Finally you can combine row and column grid to produce the magic square.

1x digit from row grid +1 + 8x digit from column grid = most perfect 8x8 magic square

0	5	2	7	0	5	2	7	0	7	6	1	2	5	4	3	1	62	51	16	17	46	35	32
6	3	4	1	6	3	4	1	6	1	0	7	4	3	2	5	55	12	5	58	39	28	21	42
5	0	7	2	5	0	7	2	1	6	7	0	3	4	5	2	14	49	64	3	30	33	48	19
3	6	1	4	3	6	1	4	7	0	1	6	5	2	3	4	60	7	10	53	44	23	26	37
0	5	2	7	0	5	2	7	1	6	7	0	3	4	5	2	9	54	59	8	25	38	43	24
6	3	4	1	6	3	4	1	7	0	1	6	5	2	3	4	63	4	13	50	47	20	29	34
5	0	7	2	5	0	7	2	0	7	6	1	2	5	4	3	6	57	56	11	22	41	40	27
3	6	1	4	3	6	1	4	6	1	0	7	4	3	2	5	52	15	2	61	36	31	18	45

The total number of squares of group 12 is: 48 (row grids H) x 6 (column grids) x 2 (swapping row and column grids) = 576; none of these squares can have the extra magic property X.

Illustration group 13

Magic squares of group 13 are constructed by means of combining 8x8 H-grids with 8x8 AC- or CA-grids.

Arbitrary we have constructed the following row grid:

H4 (row grid)

0	5	2	7	2	7	0	5
6	3	4	1	4	1	6	3
5	0	7	2	7	2	5	0
3	6	1	4	1	4	3	6
1	4	3	6	3	6	1	4
2	7	0	5	0	5	2	7
4	1	6	3	6	3	4	1
7	2	5	0	5	0	7	2

Now we must find a matching AC column grid. We start filling the top left quadrant after A1.

A1 (column grid), step 1

0	7	6	1
7	0	1	6
1	6	7	0
6	1	0	7

The 5th row needs necessarily 1-6-7-0. And you will find out that you can only finish the third quadrant successfully when following the C* structure (if you follow the A-structure you get double pairings when composing the final magic square):

A1 (column grid), step 2

0	7	6	1
7	0	1	6
1	6	7	0
6	1	0	7
1	6	7	0
7	0	1	6
0	7	6	1
6	1	0	7

Column 5 needs 2-5-3-4 or 4-3-5-2. In the example 2-5-3-4 has been chosen. With both options you can finish the upper right quadrant only successfully when following the

A-structure. The down right quadrant follows automatically, and has necessarily the C*-structure.

A1 (column grid), step 3

0	7	6	1	2	5	4	3
7	0	1	6	5	2	3	4
1	6	7	0	3	4	5	2
6	1	0	7	4	3	2	5
1	6	7	0
7	0	1	6
0	7	6	1
6	1	0	7

A1 (column grid), step 4

0	7	6	1	2	5	4	3
7	0	1	6	5	2	3	4
1	6	7	0	3	4	5	2
6	1	0	7	4	3	2	5
1	6	7	0	3	4	5	2
7	0	1	6	5	2	3	4
0	7	6	1	2	5	4	3
6	1	0	7	4	3	2	5

Finally you can combine row and column grid to produce the magic square (group 13b)

1x digit from row grid +1 + 8x digit from column grid = most perfect 8x8 magic square

0	5	2	7	2	7	0	5	0	7	6	1	2	5	4	3	1	62	51	16	19	48	33	30
6	3	4	1	4	1	6	3	7	0	1	6	5	2	3	4	63	4	13	50	45	18	31	36
5	0	7	2	7	2	5	0	1	6	7	0	3	4	5	2	14	49	64	3	32	35	46	17
3	6	1	4	1	4	3	6	6	1	0	7	4	3	2	5	52	15	2	61	34	29	20	47
1	4	3	6	3	6	1	4	1	6	7	0	3	4	5	2	10	53	60	7	28	39	42	21
2	7	0	5	0	5	2	7	7	0	1	6	5	2	3	4	59	8	9	54	41	22	27	40
4	1	6	3	6	3	4	1	0	7	6	1	2	5	4	3	5	58	55	12	23	44	37	26
7	2	5	0	5	0	7	2	6	1	0	7	4	3	2	5	56	11	6	57	38	25	24	43

In total there are 3 (A1, A2 or A3) x 2 (options of step 3) = 6 different column grids.

And, we could have started the column grid with placing a C*-quadrant in the upperleft, see new example below, group 13a:

H4 H C1* C*

1	6	3	8	3	8	1	6	0	7	6	1	2	5	4	3	1	62	51	16	19	48	33	30
7	4	5	2	5	2	7	4	6	1	0	7	4	3	2	5	55	12	5	58	37	26	23	44
6	1	8	3	8	3	6	1	1	6	7	0	3	4	5	2	14	49	64	3	32	35	46	17
4	7	2	5	2	5	4	7	7	0	1	6	5	2	3	4	60	7	10	53	42	21	28	39
2	5	4	7	4	7	2	5	0	7	6	1	2	5	4	3	2	61	52	15	20	47	34	29
3	8	1	6	1	6	3	8	7	0	1	6	5	2	3	4	59	8	9	54	41	22	27	40
5	2	7	4	7	4	5	2	1	6	7	0	3	4	5	2	13	50	63	4	31	36	45	18
8	3	6	1	6	1	8	3	6	1	0	7	4	3	2	5	56	11	6	57	38	25	24	43

H H A1 A

This possibility gives another 6 column grids. Note that starting with C2*, C4*, and C6* top left does not lead to matching grids.

So, the total number of squares of group 13a +13b is: 48 (row grids H) x 12 (column grids AC or CA) x 2 (swapping row and column grids) = 1152.

Illustration group 14

Magic squares of group 14 can be constructed by combining K-grids with B-grids.

The construction of row and column grids is similar to group 11.

See the following example:

1x digit from row grid +1 + 8x digit from column grid = most perfect 8x8 magic square

0	7	1	6	0	7	1	6	0	1	6	7	2	3	4	5	1	16	50	63	17	32	34	47
3	4	2	5	3	4	2	5	6	7	0	1	4	5	2	3	52	61	3	14	36	45	19	30
6	1	7	0	6	1	7	0	1	0	7	6	3	2	5	4	15	2	64	49	31	18	48	33
5	2	4	3	5	2	4	3	7	6	1	0	5	4	3	2	62	51	13	4	46	35	29	20
4	3	5	2	4	3	5	2	0	1	6	7	2	3	4	5	5	12	54	59	21	28	38	43
7	0	6	1	7	0	6	1	6	7	0	1	4	5	2	3	56	57	7	10	40	41	23	26
2	5	3	4	2	5	3	4	1	0	7	6	3	2	5	4	11	6	60	53	27	22	44	37
1	6	0	7	1	6	0	7	7	6	1	0	5	4	3	2	58	55	9	8	42	39	25	24

The total amount of squares of group 14 is 576.

Illustration group 15

Magic squares of group 15 are constructed by combining K-grids with C-grids.

The construction of row and column grids is similar to group 12.

See the following example (note that the row grid is the same as in the example of group 14):

1x digit from row grid +1 + 8x digit from column grid = most perfect 8x8 magic square

0	7	1	6	0	7	1	6	0	4	3	7	1	5	2	6	1	40	26	63	9	48	18	55
3	4	2	5	3	4	2	5	7	3	4	0	6	2	5	1	60	29	35	6	52	21	43	14
6	1	7	0	6	1	7	0	4	0	7	3	5	1	6	2	39	2	64	25	47	10	56	17
5	2	4	3	5	2	4	3	3	7	0	4	2	6	1	5	30	59	5	36	22	51	13	44
4	3	5	2	4	3	5	2	4	0	7	3	5	1	6	2	37	4	62	27	45	12	54	19
7	0	6	1	7	0	6	1	3	7	0	4	2	6	1	5	32	57	7	34	24	49	15	42
2	5	3	4	2	5	3	4	0	4	3	7	1	5	2	6	3	38	28	61	11	46	20	53
1	6	0	7	1	6	0	7	7	3	4	0	6	2	5	1	58	31	33	8	50	23	41	16

The total amount of squares of group 15 is 576.

Illustration group 16

Magic squares of group 16 are constructed by combining K-grids with BC- and CB-grids.

The construction of row and column grids is similar to group 13.

See the following example, group 16a:

1x digit from row grid +1 + 8x digit from column grid = most perfect 8x8 magic square

0	7	1	6	0	7	1	6	0	4	3	7	2	6	1	5	1	40	26	63	17	56	10	47
3	4	2	5	3	4	2	5	7	3	4	0	5	1	6	2	60	29	35	6	44	13	51	22
6	1	7	0	6	1	7	0	4	0	7	3	6	2	5	1	39	2	64	25	55	18	48	9
5	2	4	3	5	2	4	3	3	7	0	4	1	5	2	6	30	59	5	36	14	43	21	52
6	1	7	0	6	1	7	0	0	4	3	7	2	6	1	5	7	34	32	57	23	50	16	41
3	4	2	5	3	4	2	5	3	7	0	4	1	5	2	6	28	61	3	38	12	45	19	54
0	7	1	6	0	7	1	6	4	0	7	3	6	2	5	1	33	8	58	31	49	24	42	15
5	2	4	3	5	2	4	3	7	3	4	0	5	1	6	2	62	27	37	4	46	11	53	20

The total amount of squares of group 16a + 16b is 576 + 576 =1152.

Illustration group 17

Magic squares of group 17 are constructed by combining HK- or KH-grids with CB- or BC- grids.

Again is emphasized that only half of the 96 HK row grids can be successfully combined with C*B column grid. Below you see an arbitrary chosen HKHK-row grid.

H4 (row grid) K4

0	5	2	7	0	7	2	5
6	3	4	1	6	1	4	3
5	0	7	2	5	2	7	0
3	6	1	4	3	4	1	6
4	1	6	3	4	3	6	1
2	7	0	5	2	5	0	7
1	4	3	6	1	6	3	4
7	2	5	0	7	0	5	2

Now a matching CB column grid must be found. Start with putting C1*, C3* or C5* in

the upper left quadrant. It is useful to verify that C2*, C4* and C6* will immediately bring you in trouble when trying to develop the upper right quadrant! In the example C1* has been chosen.

C1* (column grid), step 1

0	7	6	1
6	1	0	7
1	6	7	0
7	0	1	6

In the 5th row you can only continue with 1-6-7-0. With this the down left quadrant can only be finished successfully maintaining the C*-structure. (Verify that the A-structure does not work!):

C1* (column grid), step 2

0	7	6	1
6	1	0	7
1	6	7	0
7	0	1	6
1	6	7	0
7	0	1	6
0	7	6	1
6	1	0	7

In column 5 only 2-4-3-5 or 4-2-5-3 are possible. With both options you can finish the upper right quadrant succesfully, but only when following the B-structure. In the example 4-2-5-3 has been chosen. The down right quadrant follows automatically, and has necessarily also the B-structure.

C1* (column grid), step 3

0	7	6	1	4	5	2	3
6	1	0	7	2	3	4	5
1	6	7	0	5	4	3	2
7	0	1	6	3	2	5	4
1	6	7	0
7	0	1	6
0	7	6	1
6	1	0	7

C1* (column grid), step 4

0	7	6	1	4	5	2	3
6	1	0	7	2	3	4	5
1	6	7	0	5	4	3	2
7	0	1	6	3	2	5	4
1	6	7	0	5	4	3	2
7	0	1	6	3	2	5	4
0	7	6	1	4	5	2	3
6	1	0	7	2	3	4	5

In total there are 3 (C1*, C3*, C5*) x 2 (options of step 3) = 6 different column grids.

Finally you can combine row and column grid to produce the magic square.

1x digit from row grid +1 + 8x digit from column grid = most perfect 8x8 magic square

0	5	2	7	0	7	2	5	0	7	6	1	4	5	2	3	1	62	51	16	33	48	19	30
6	3	4	1	6	1	4	3	6	1	0	7	2	3	4	5	55	12	5	58	23	26	37	44
5	0	7	2	5	2	7	0	1	6	7	0	5	4	3	2	14	49	64	3	46	35	32	17
3	6	1	4	3	4	1	6	7	0	1	6	3	2	5	4	60	7	10	53	28	21	42	39
4	1	6	3	4	3	6	1	1	6	7	0	5	4	3	2	13	50	63	4	45	36	31	18
2	7	0	5	2	5	0	7	7	0	1	6	3	2	5	4	59	8	9	54	27	22	41	40
1	4	3	6	1	6	3	4	0	7	6	1	4	5	2	3	2	61	52	15	34	47	20	29
7	2	5	0	7	0	5	2	6	1	0	7	2	3	4	5	56	11	6	57	24	25	38	43

The total amount of squares of above combination is: 48 (row grids HKHK) x 6 (column grids C*BC*B) x 2 (swapping row and column grids) = 576. And, of course, the same amount may be generated with the combination KHKH/BC*BC*. So, the total amount of squares of group 17a+b is 1152.

Illustration group 18

Magic squares of group 18 are constructed by combining HK- and KH-grids with AC- and CA-grids.

See below the same row grid as was chosen for group 17.

H4 (row grid) K4

0	5	2	7	0	7	2	5
6	3	4	1	6	1	4	3
5	0	7	2	5	2	7	0
3	6	1	4	3	4	1	6
4	1	6	3	4	3	6	1
2	7	0	5	2	5	0	7
1	4	3	6	1	6	3	4
7	2	5	0	7	0	5	2

Now we are going to find a matching AC column grid. Put the 0-quadrant A1, A2 or A3 in the upper left corner. In the example A1 has been chosen.

A1 (column grid), step 1

0	7	6	1
7	0	1	6
1	6	7	0
6	1	0	7

In the 5th row only 0-7-6-1 is possible. With this the down left quadrant can only be finished successfully maintaining the A-structure. (Verify that a C*-structure does not

work!):

A1 (column grid), step 2

0	7	6	1
7	0	1	6
1	6	7	0
6	1	0	7
0	7	6	1
7	0	1	6
1	6	7	0
6	1	0	7

In column 5 only 2-5-3-4 or 4-3-5-2 are possible. With both options you can finish the upper right quadrant, but only when following the C-structure. Then the down right quadrant follows automatically, and has necessarily also the C-structure. In the example 4-3-5-2 has been chosen.

A1 (column grid), step 3

0	7	6	1	4	5	2	3
7	0	1	6	3	2	5	4
1	6	7	0	5	4	3	2
6	1	0	7	2	3	4	5
0	7	6	1
7	0	1	6
1	6	7	0
6	1	0	7

A1 (column grid), step 4

0	7	6	1	4	5	2	3
7	0	1	6	3	2	5	4
1	6	7	0	5	4	3	2
6	1	0	7	2	3	4	5
0	7	6	1	4	5	2	3
7	0	1	6	3	2	5	4
1	6	7	0	5	4	3	2
6	1	0	7	2	3	4	5

In total there are 3 (A1, A2, A3) x 2 (options of step 3) = 6 different column grids.

Finally you can combine row and column grid to produce the magic square.

1x digit from row grid +1 + 8x digit from column grid = most perfect 8x8 magic square

0	5	2	7	0	7	2	5	0	7	6	1	4	5	2	3	1	62	51	16	33	48	19	30
6	3	4	1	6	1	4	3	7	0	1	6	3	2	5	4	63	4	13	50	31	18	45	36
5	0	7	2	5	2	7	0	1	6	7	0	5	4	3	2	14	49	64	3	46	35	32	17
3	6	1	4	3	4	1	6	6	1	0	7	2	3	4	5	52	15	2	61	20	29	34	47
4	1	6	3	4	3	6	1	0	7	6	1	4	5	2	3	5	58	55	12	37	44	23	26
2	7	0	5	2	5	0	7	7	0	1	6	3	2	5	4	59	8	9	54	27	22	41	40
1	4	3	6	1	6	3	4	1	6	7	0	5	4	3	2	10	53	60	7	42	39	28	21
7	2	5	0	7	0	5	2	6	1	0	7	2	3	4	5	56	11	6	57	24	25	38	43

The total amount of squares of above combination HKHK/ACAC is: 48 (row grids HK) x 6 (column grids) x 2 (swapping row and column grids) = 576. The combination KHKH/CACA gives the same amount, so the total amount of group 18 is 1152.

Illustration group 19

Magic squares of group 19 are constructed by combining HK- or KH-grids with grids consisting of A-, B-, C- and C*-quadrants.

See below the following row grid (the grid is almost the same as in previous examples, only row 6 and 8 have been swapped).

H4 (row grid) K4

0	5	2	7	0	7	2	5
6	3	4	1	6	1	4	3
5	0	7	2	5	2	7	0
3	6	1	4	3	4	1	6
4	1	6	3	4	3	6	1
7	2	5	0	7	0	5	2
1	4	3	6	1	6	3	4
2	7	0	5	2	5	0	7

Again we are going to find a matching column grid starting with an A-structure in the upper left. In the example A1 has been chosen.

A1 (column grid), step 1

0	7	6	1
7	0	1	6
1	6	7	0
6	1	0	7

In the 5th row only 0-7-6-1 is possible. And now we find out that the down left quadrant can only be finished successfully when following a C*-structure ( the A-structure does not work, verify!):

A1 (column grid), step 2

0	7	6	1
7	0	1	6
1	6	7	0
6	1	0	7
0	7	6	1
6	1	0	7
1	6	7	0
7	0	1	6

C1*

The right half of the row grid must be filled with the digits 2, 3, 4, and 5. In column 5 only 2-5-3-4 and 4-3-5-2 are possible. With both options you can finish the upper right

quadrant successfully, but only when following the C-structure. Then the down

right quadrant follows automatically, and has necessarily the B-structure. In

the example 4-3-5-2 has been chosen.

A1 (column grid), step 3

0	7	6	1	4	5	2	3
7	0	1	6	3	2	5	4
1	6	7	0	5	4	3	2
6	1	0	7	2	3	4	5
0	7	6	1
6	1	0	7
1	6	7	0
7	0	1	6

C1*

A1 (column grid), step 4

0	7	6	1	4	5	2	3
7	0	1	6	3	2	5	4
1	6	7	0	5	4	3	2
6	1	0	7	2	3	4	5
0	7	6	1	4	5	2	3
6	1	0	7	2	3	4	5
1	6	7	0	5	4	3	2
7	0	1	6	3	2	5	4

C1*

In total there are 3 (A1, A2, A3) x 2 (options of step 3) = 6 different column grids.

Finally you can combine row and column grid to produce the magic square:

1x digit from row grid +1 + 8x digit from column grid = most perfect 8x8 magic square

0	5	2	7	0	7	2	5	0	7	6	1	4	5	2	3	1	62	51	16	33	48	19	30
6	3	4	1	6	1	4	3	7	0	1	6	3	2	5	4	63	4	13	50	31	18	45	36
5	0	7	2	5	2	7	0	1	6	7	0	5	4	3	2	14	49	64	3	46	35	32	17
3	6	1	4	3	4	1	6	6	1	0	7	2	3	4	5	52	15	2	61	20	29	34	47
4	1	6	3	4	3	6	1	0	7	6	1	4	5	2	3	5	58	55	12	37	44	23	26
7	2	5	0	7	0	5	2	6	1	0	7	2	3	4	5	56	11	6	57	24	25	38	43
1	4	3	6	1	6	3	4	1	6	7	0	5	4	3	2	10	53	60	7	42	39	28	21
2	7	0	5	2	5	0	7	7	0	1	6	3	2	5	4	59	8	9	54	27	22	41	40

Above combination HKHK/ACC*B (combination 19a) generates 48 x 6 x 2 = 576 squares.

In the above example we started the column grid with an A-structure. It is evident that

we can also start the column grid with a C*-structure. Then you get for example:

H4 K4 C3* B

0	5	2	7	0	7	2	5	0	7	5	2	4	6	1	3	1	62	43	24	33	56	11	30
6	3	4	1	6	1	4	3	5	2	0	7	1	3	4	6	47	20	5	58	15	26	37	52
5	0	7	2	5	2	7	0	2	5	7	0	6	4	3	1	22	41	64	3	54	35	32	9
3	6	1	4	3	4	1	6	7	0	2	5	3	1	6	4	60	7	18	45	28	13	50	39
4	1	6	3	4	3	6	1	2	5	7	0	6	4	3	1	21	42	63	4	53	36	31	10
7	2	5	0	7	0	5	2	5	2	0	7	1	3	4	6	48	19	6	57	16	25	38	51
1	4	3	6	1	6	3	4	0	7	5	2	4	6	1	3	2	61	44	23	34	55	12	29
2	7	0	5	2	5	0	7	7	0	2	5	3	1	6	4	59	8	17	46	27	14	49	40

H K A C

Also this combination HKHK/C*BAC (combination 19b) gives 576 squares. This makes together 1152 squares.

And, finally, we can repeat the whole reasoning above with a KHKH row grid (combinations 19c and 19d). And again this will give 1152 new squares.

So, the total amount of squares of group 19a+b+c+d is 2304.

8x8, Quadrant method, group 11 up to 19.

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8x8 magic square